Friction Between Solids

April 2008, published 28, doi: 10.1098/rsta.2007.2169366 2008 Phil. Trans. R. Soc. A

MikulskiJudith A Harrison, Guangtu Gao, J.David Schall, M. Todd Knippenberg and Paul T Friction between solids

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Friction between solids

BY JUDITH A. HARRISON1,*, GUANGTU GAO

1, J. DAVID SCHALL1,

M. TODD KNIPPENBERG1

AND PAUL T. MIKULSKI2

1Department of Chemistry, and 2Department of Physics,United States Naval Academy, Annapolis, MD 21402, USA

The theoretical examination of the friction between solids is discussed with a focus onself-assembled monolayers, carbon-containing materials and antiwear additives.Important findings are illustrated by describing examples where simulations havecomplemented experimental work by providing a deeper understanding of the molecularorigins of friction. Most of the work discussed herein makes use of classical moleculardynamics (MD) simulations. Of course, classical MD is not the only theoretical toolavailable to study friction. In view of that, a brief review of the early models of frictionis also given. It should be noted that some topics related to the friction between solids,i.e. theory of electronic friction, are not discussed here but will be discussed in asubsequent review.

Keywords: atomic-scale friction; molecular dynamics; diamond; tribochemistry;SAMS; adhesion

Onnan

*A

1. Introduction

The field of tribology is one of the oldest, dating back to the construction of theEgyptian pyramids. The modern study of tribology began with Leonardo daVinci (1452–1519) when he deduced the laws governing the motion of arectangular block sliding over a planar surface (Dowson 1998; Krim 2002). Sinceda Vinci’s work was unpublished, these observations were rediscovered byAmontons in 1699. His two basic laws of friction are: (i) friction force isproportional to the normal load and (ii) the friction force is independent of thecontact area. In 1781, Coulomb verified these observations and determined thatthe friction force is independent of velocity for ordinary sliding speeds.

Despite the fact that these friction laws hold for a variety of macroscopicsystems, they have defied attempts to explain them on a fundamental (ormicroscopic) level (Krim 2002). The advent of new experimental techniques toexamine the fundamental aspects of friction has renewed interest in the field oftribology in the last few decades. One of the first experimental techniques tobe developed for the fundamental studies of friction was the surface forceapparatus (SFA; Ruths & Israelachvili 2007). Other techniques include thequartz crystal microbalance (QCM; Krim & Widom 1988) and scanning probe

Phil. Trans. R. Soc. A (2008) 366, 1469–1495

doi:10.1098/rsta.2007.2169

Published online 20 December 2007

e contribution of 8 to a Theme Issue ‘Nanotribology, nanomechanics and applications tootechnology I’.

uthor for correspondence ([email protected]).

1469 This journal is q 2007 The Royal Society


J. A. Harrison et al.1470


microscopies (Binnig et al. 1986; Carpick & Salmeron 1997; Gnecco et al. 2007).While all these techniques have played pivotal roles in the examination ofthe fundamental origins of friction, the atomic force microscope (AFM) is,perhaps, the most widely used technique. The AFM is used to investigate theforces present, as a small tip is moved across a surface. Even with carefulcalibration, AFM experiments do not provide a complete picture of theindividual forces between a given tip and surface atom. As computationaltechniques, e.g. molecular dynamics (MD), provide information about eachatom present at a sliding interface, they are uniquely suited to complementexperimental techniques.

2. Molecular dynamics

In contrast to quantum dynamics, classical MD deals with approximateinteratomic forces. The basic set-up of MD algorithms is straightforward andhas been discussed in a number of reviews (Harrison et al. 1999; Robbins &Muser 2001; Heo et al. 2005). In this technique, atoms are treated as discreteparticles. The force on each atom is calculated after determining the systemgeometry, the positions and velocities of each atom and the boundary conditions.Atomic forces can be calculated by taking the derivative of an analyticinteratomic potential energy function with respect to position or by usingquantum mechanical methods (Car & Parrinello 1985). Analytic potential energyfunctions in classical MD simulations have proven to be very useful in simulatinga wide range of phenomena. The choice of the potential energy function is criticalto any simulation. The ideal potential energy function would have a simple formso that it would not be computationally intensive while capturing the essentialphysics and chemistry of the process of interest. The focus of this paper isclassical MD simulations which make use of these potentials; however, quantumMD is briefly discussed.

3. Static versus kinetic friction

The force that is required to maintain a sliding velocity v over a certain distance dis the kinetic friction. The sliding velocity plays a major role in the kinetic friction.For the sliding of two contacts at low velocities, with a small layer of fluid confinedin between the layers, the kinetic friction at the microscopic scale is seen to increaselinearly with the velocity (Krim et al. 1991; Smith et al. 1996; Mak & Krim 1998).This linear response of friction can be described with the following equation:

F ZM

tv; ð3:1Þ

whereM is the mass of the sliding object; t is the slip time or the time required for amoving object to slow to 1/e of the original sliding speed (Krim & Widom 1988);and v is the sliding speed. However, as the velocity increases, the friction no longerobeys this linear relation.

As a sliding surface moves across the stationary surface, the kinetic energy ofthe sliding surface is transferred to the stationary surface, causing a temperatureincrease. This increase can alter the face of the stationary surface, affecting the

Phil. Trans. R. Soc. A (2008)


1471Friction between solids


rate at which friction increases with velocity. At intermediate velocities, thekinetic friction is given by

FkzFkðvrefÞCc lnv0vref

� �g

; ð3:2Þ

where c is a constant; vref is the reference velocity; v0 is the sliding velocity; and gis an exponent that is approximately 1 (Muser 2006). At high sliding velocities,the transfer of heat could become too slow to have any effect on the friction, asthe sliding surface has moved past the point of heat transfer of the stationarysurface. When this occurs, the friction deviates from linearity.

Static friction is the force required to initiate sliding. The existence of thisforce suggests that the two surfaces are interlocked into a local free energyminimum. The friction force is the lateral force required to lift the surfaces outof the local minimum. However, there is a fundamental problem with thisexplanation. There is no reason why the peaks and troughs in surface free energybetween surfaces should be correlated (except in the exceedingly rare case oflattice commensurability). One expects that at any moment of time, some peaksare moving up a ramp while others are moving down. The net lateral forceaverages to zero and there should be no static friction. Analytic and simulationstudies of clean crystalline and disordered structures have supported thisargument. However, macro-scaled objects almost always exhibit a finite staticfriction. Simulations have shown that the prevalence of static friction can beexplained by third bodies, like hydrocarbons, which absorb on any surfaceexposed to ambient air and lock the surfaces together (He et al. 1999). Staticfriction was determined by either ramping or stepping the force until the systembegan to slide. A commensurate and a number of incommensurate surfaces withadsorbates were examined. In all the simulations, a finite value of static frictionwas observed. Every incommensurate system had approximately the same staticfriction with respect to a given normal load, independent of sliding direction.This indicated that the friction force is independent of surface orientation. Onlythe commensurate case produced different results with higher static friction, asexpected, due to the uniform registry between the two surfaces.

4. Friction of crystalline surfaces

(a ) Friction of diamond

The properties of diamond, such as excellent thermal conductivity, corrosion andwear resistance, and surface stability, have generated tremendous scientific andtechnological interest. The advent of chemical vapour deposition has sparkedinterest in diamond as a thin film coating for flat-panel displays, cutting tools,bearings and for micro- and nanoelectromechanical systems. Its hardness andresistance to wear makes it particularly attractive for tribological applications.As a result, it has become important to understand the friction and wearproperties of diamond and diamond coatings.

Complex processes at sliding interfaces, such as roughness, grain size, surfaceorientation and chemical composition, can play a role in determining the surfacefriction. Historically, it has been proven difficult to separate the effects on friction





due to individual experimental variables using traditional macroscopictribological experiments. In contrast, modern nanoscale AFM measurementsand MD simulations provide an opportunity to vary individual parameters, suchas load, contact pressure, sliding direction, sliding speed and environment, togain insight into the fundamental friction mechanisms of diamond.

Energy dissipation in diamond systems was examined using MD (Harrisonet al. 1995; Perry & Harrison 1995). When two diamond surfaces were in slidingcontact, opposing atoms interact. The friction force varied with the periodicityof the atomic lattice and the maxima corresponded to points of stronginteraction (mechanical deformation) between hydrogen atoms on opposingsurfaces. The vibrational excitation (heating) of the surface bonds generated bythis interaction is the essence of wearless friction. In general, this excitationincreased with increasing load, causing an increase in atomic-scale friction.Several ways to alter the vibrational excitation of the interface during slidingwere identified. These include replacing a few hydrogen atoms on the surface ofthe diamond with chemically bound methyl, ethyl and n-propyl groups(Harrison et al. 1993) or placing third body molecules, such as methane,ethane etc., in between the surfaces (Perry & Harrison 1997) in sliding contact.In general, the trapped third body molecules reduced friction to a greater extentthan chemically bound groups. The trapped molecules acted as a boundarylayer lubricant keeping the sliding surfaces apart and thereby reducing thevibrational excitation. The smallest molecule examined, methane, produced thelargest reduction in friction because its small size and flexibility made it easierto avoid the strong collisions with the surface molecules during sliding. Incontrast, chemically attaching groups to diamond reduced their ability to avoidstrong collisions with the surface. In that case, the larger attached groupsreduced friction more due to the increased flexibility that comes with increasingthe length of the carbon atom chain.

There are several ways in which the conditions of these early simulations werenot well-matched to nanoscale experiments. For example, both contactingsurfaces were infinitely flat. Thus, the application of load caused the uniformcompression of both materials over a constant contact area, rather than non-uniform compression of the materials and a varying contact area with loadthat occurs with a curved surface. Recently, a joint MD-AFM study ofdiamond(001)(2!1)-H and diamond(111)(1!1)-H was undertaken where theconditions were designed to correspond as closely as possible (Gao et al. 2007).Wearless friction as a function of load, surface orientation and sliding directionon individual crystalline grains of diamond was examined. The simulations usedthe second-generation reactive empirical bond-order (REBO) potential, whichreproduces the zero Kelvin elastic constants of diamond (Brenner et al. 2002). Asthe extraction of shear strengths from AFM data using continuum theoryrequires knowledge of the mechanical properties of the tip and the sample, theaccurate modelling of the elastic properties is central to the correspondencebetween the simulation and the experiment.

The AFM measurements showed higher adhesion and friction forces for (001)versus (111) surfaces. However, the increased friction forces were entirelyattributed to increased contact area induced by higher adhesion. No difference inthe intrinsic resistance to friction, i.e. in the interfacial shear strength, wasobserved. The MD results showed no significant difference in friction between the





two diamond surfaces, except for the specific case of sliding at high pressuresalong the dimer row direction ([�110]) on the (001) surface (i.e. perpendicular tothe dimer C–C bond). Both the AFM and MD results showed that nanoscaletribological behaviour deviates dramatically from the established macroscopicbehaviour of diamond, which is highly dependent on orientation. While the tipsizes, contact pressures, sliding speeds and precise atomic structures of the tipsused in the MD simulations and the AFM experiments were different, the resultswere, nonetheless, essentially in agreement.

The MD simulations predicted that sliding perpendicular to the C–C dimerbonds on diamond(001) (along the [�110] direction) yields lower average frictionat high loads than when sliding parallel to the bonds (along the [110] direction)under certain conditions. Changing the tip geometry from curved to flatexacerbated this difference. This study demonstrated that the tip shape, andperhaps size, can mask or enhance this friction difference. (Reducing the size ofthe AFM tip also reduced the interfacial shear strength in this direction;however, it was not statistically different in any direction.) The larger spacingbetween the surface hydrogen atoms perpendicular to the dimer bond, and thedifferent orientation of the carbon-hydrogen bond, allows the surface hydrogenatoms more freedom, depending upon the contact geometry of the tip, and thusfriction can be lower when sliding in this direction. A second contribution couldbe due to the overall increased corrugation of the surface potential along thedimer bond, due to the dimer rows and the troughs between them, whichincreases the potential barrier that must be overcome to initiate sliding, andincreases the probability of stick–slip energy dissipation.

(b ) Simple models, stick–slip and superlubricity

Atomic-scale stick–slip has been observed experimentally, in simulations, andis predicted by simple friction models. The first experimental observation ofatomic-scale stick–slip was obtained by Mate et al. (1987) using an AFM with atungsten tip in sliding contact with the basal plane of graphite. Subsequently,many observations of atomic-scale stick–slip have been made on a variety ofsubstrates (e.g. Carpick & Salmeron 1997; Gnecco et al. 2007) includingdiamond (Germann et al. 1993). Insight into the atomic-scale stick–slipphenomenon has been provided by MD simulations of two contacting diamondsurfaces (Harrison et al. 1992a, 1995), of a tip and a Si surface (Landman et al.1989), metal surfaces (Sorensen et al. 1996) and two infinite surfaces of organicmonolayers in sliding contact (Glosli & McClelland 1993; Mikulski & Harrison2001a,b; Chandross et al. 2004; Harrison et al. 2004; Mikulski et al. 2005a,b).

Various simple models of friction have also been used to explain ‘wearlessfriction’ and atomic-scale stick–slip (Tomlinson 1929; Frenkel & Kontorova1938; Braun & Naumovets 2006). In the Tomlinson model, two atomically flatsolids, A and B, are in sliding contact. The B solid has surface atoms (denoted asB0) attached to it by harmonic springs, which can lose energy to the supportthrough vibration. As the surfaces slide, any given B0 atom experiences thepotential, VAB, arising from the interaction of the two surfaces. It is the shape ofVAB that ultimately governs the friction process. For strongly interactingsurfaces, VAB will contain various local extrema. A given B0 atom passes thoughvarious metastable local minima upon sliding and may become ‘stuck’. Falling





from these metastable minima to a lower minimum causes B0 to becomevibrationally excited. This process is the ‘slip’ and has also been termed‘plucking’. The vibrational energy is then dissipated to the solid as heat.Therefore, plucking results in the strain energy of translation being converted tovibrational energy, which is the essence of the atomic-scale friction process. Forvery weakly interacting solids, the friction vanishes since VAB would contain nometastable local minima.

Computer simulations can shed additional insight into the earlier models ofwearless friction. For example, the directional dependence of friction is implicit tothe simple models of friction because a different placement of atoms implies adifferent interaction potential governing the friction process. Different atomplacements are encountered when sliding in the [110] direction of adiamond(111)(1!1)-H surface versus the [112] direction. Therefore, simplemodels would predict that the friction should be different in these two directions.In contrast, simulations and experiments indicate that other factors, such ascontact area and surface alignment, must also be considered. In contrast to thepredictions of the simple models, AFM measurements of the wearless friction ofdiamond(111)(1!1)-H and (001)(2!1)-H show no inherent friction differences asa function of sliding direction (Gao et al. 2007). When MD simulation conditionsare designed to closely correlate with experimental conditions (finite-sized tipsand the sampling of multiple configurations), the friction of diamond(111) and(001) is independent of sliding direction except for the one case mentioned earlier.However, when two infinitely flat surfaces are in sliding contact and multipleconfigurations are not sampled simulations, the friction of diamond(111) isanisotropic, which is consistent with the simple models of wearless friction(Harrison et al. 1992a). This geometry would be similar to an AFM single-linescan with a very small tip (or with a flake attached), where commensurate contactcould be achieved. These results suggest that results obtained with smaller AFMtips may more closely match predictions from simple models.

For crystalline surfaces, it is clear that atomic-scale stick–slip also depends onthe load. Microscopic measurements of friction in ultra high vacuum (UHV)between a Si tip in contact with NaCl(100) provide the experimentalconfirmation that when the load is reduced, and the surface interaction potentialchanges sufficiently, a transition from stick–slip to smooth sliding occurs(Socoliuc et al. 2004). When the two surfaces are commensurate and the load isappreciable, stick–slip can result. When two incommensurate surfaces are insliding contact, superlubricity or a state of extraordinarily low friction can occur.Hirano & Shinjo (1990) were the first to suggest that the interaction potentialbetween two surfaces, VAB, could be reduced by making the surfacesincommensurate. Subsequent experiments examined the friction betweenmuscovite mica sheets as a function of lattice misfit angle revealed that thefriction was anisotropic and displayed periodicity consistent with the hexagonalsymmetry of mica (Hirano et al. 1991).

Several accounts of the experimental observation of superlubricity haveappeared in the literature. Martin et al. (1993) examined MoS2 in UHV andfound ultralow friction coefficients (approx. 10K3). Scanning tunnellingmicroscopy measurements in UHV (Hirano et al. 1997) of a W(011) wire incontact with Si(001) showed that the friction is below the detection limit forincommensurate contacts. Recently, Dienwiebel et al. (2004) used a novel friction





force microscope, which allows for quantitative measurement of the friction forcein three directions, to examine friction between a tungsten tip and graphite. Thiswork clearly demonstrated that the peaks in the friction occurred at 08 and 608scanning angles and vanished for all other angles. This result is consistent withthe simple models of wearless friction described above. Mate et al. (1987) hadspeculated that the atomic-scale periodicity apparent in their friction scans wascaused by a graphite flake that had adhered to the tip of the AFM, thus creatinga graphite–graphite sliding interface. Despite a post-friction experimenttransmission electron microscopy (TEM) analysis of the tip by Dienwiebelet al. (2004, 2005), no evidence of the flake was obtained. Recent in situ TEManalysis of a tungsten tip sliding against graphite has demonstrated the existenceof a graphite flake on the tip during sliding (Merkle & Marks 2007). For a morecomplete discussion on the friction between commensurate and incommensuratecontacts, the reader is referred to Muser (2006) and Muser & Robbins (2000).

In commensurate contacts, the interfacial energy is a periodic function ofsliding distance because the relative alignment of atoms in each surface changesin phase as the surfaces slide past each other. Incommensurate contacts can beachieved in identical materials with different crystallographic orientations or indifferent materials with different lattice constants. In this case, the interfacialpotential samples all the relative positions of all the surface atoms. Energy isindependent of sliding distance and there is no static friction. The ‘cobblestone’model (Homola et al. 1990) offers a simple explanation for this behaviour. As acart wheel (or atom) rolls across a cobble stone street, energy is dissipated as thewheel rolls down rapidly down from the top of the cobblestone (or a peak in thesurface potential) into the cracks between the cobbles and is stopped by the nextcobble (or next peak in the surface potential). In the case of the commensuratelattice, all the wheels (or atoms) of the cart fall into the cracks at the same timeand a significant amount of the cart’s potential energy is dissipated. In theincommensurate case, only one wheel (or atom) falls into the crack at a time andonly a fraction of the potential energy is dissipated. This potential corrugationcan pin two surfaces together and prevent motion. Muser & Robbins (2000)modelled pinning between commensurate and incommensurate surfaces usingMD. Two surfaces were brought together and the top surface was allowed todiffuse over the bottom surface. Commensurate surfaces were always pinned by aperiodic potential when the total surface potential grew with increased systemsize. However, relatively large systems may be unpinned if the surface potentialis small enough. Incommensurate surfaces were completely unpinned unless theyhave very high elastic compliance.

Experiments of carbon nanotube rolling and sliding on graphite have shownthat nanotubes have preferred orientations on graphite substrates (Falvo et al.1999). These experiments showed that nanotubes preferred to roll whenin-registry and slide while out-of-registry. Resisting forces measured while thenanotubes were sliding were significantly lower than those measured duringrolling. Simulations of a carbon nanotube on graphite surfaces by Schall &Brenner (2000) showed that the difference in observed friction arises from thecorrugation of the potential energy surface that the nanotube encounters as itmoves across the graphite. When in-registry, the lattices of the graphite andnanotube are aligned commensurately so that the surface energy is deeplycorrugated. For the nanotube to move, it must either climb out of this deep





potential well or roll. When out-of-registry, the potential corrugation isminimized and the nanotube easily slides along the substrate with very littleresistance. This same effect has been used to explain the lubricating properties ofgraphite (Dienwiebel et al. 2004, 2005).

5. Tribochemistry

Placing two solid bodies in sliding contact can result in wear, often with theformation of debris. The nascent particles that form the debris can interactfurther, either physically or chemically, with the solid bodies or other nascentparticles. This interaction of chemistry and friction is known as tribochemistry,the results of which are well known in everyday life—combustion engines breakdown, cutting tools become dull and bearings fail. Despite the obviousimportance of these consequences, and the long history of the field of tribology,a full understanding of the atomic-scale mechanisms responsible for friction-induced wear remains elusive.

Historically, characterization of reactions that occur during sliding has provendifficult due to the fact that the sliding interfaces are typically buried andtraditional analysis methods were restricted to examination of the contact regionsubsequent to sliding. The resurgence of the field of tribology has spurred thedevelopment of experimental methods to examine the chemistry that occurs at aninterface during sliding. For example, an in situ analysis of the tribochemistrybetween diamond-like carbon (DLC) surfaces was carried out byOlsen et al. (1996)using internal reflection spectroscopy. This apparatus allowed for the character-ization of intermediates and products formed during sliding. Scharf& Singer (2002)used in situ Raman spectroscopy coupled to a tribometer to examine the role ofthird bodies in the friction behaviour of diamond-like carbon.While examining theinterface during sliding is preferable, it is not always possible. New techniques arebeing employed to perform careful post-mortem analysis of the sliding region. Forinstance, Carpick and co-workers have used X-ray photo-emission electronmicroscopy to examine inside and outside the wear track of ultrananocrystallinediamond. Erdemir & Eryilmaz (2007) have used time-of-flight secondary ion massspectroscopy to obtain two- and three-dimensional maps of the wear track of DLCfilms. These maps provide evidence of hydrocarbon fragments within the weartracks of highly hydrogenated DLC films. While monitoring reactants, theformation of intermediates and product formation has proven to be anexperimental challenge, MD simulations are uniquely suited to this task.

(a ) Chemical reactions between diamond surfaces

The study of tribochemistry using classical MD simulations requires the use ofa potential energy function that is capable of modelling chemical reactions or theuse of quantum methods (Koskilinna et al. 2005; Mosey et al. 2005; Koyama et al.2006) to calculate the forces. The bond-order potentials (Brenner 1990; Stuartet al. 2000) are able to model chemical reactions in covalent materials and arethus suited to model tribochemistry.

A glimpse into the rich, non-equilibrium tribochemistry that occurs when twodiamond surfaces are in sliding contact was reported by Harrison & Brenner(1994). In one set of simulations, two diamond(111)(1!1)-H surfaces were in



Figure 1. Close-up of the interface region between two diamond(111)(1!1)-H surfaces in slidingcontact. The upper surface began the simulation with two H atoms replaced by ethyl groups. Ahydrocarbon debris molecule and an H2 molecule are the tribochemical products at the end of thesimulation. Adapted with permission from Harrison & Brenner (1994).



sliding contact. In the second set, two hydrogen atoms of the upper surfacewere replaced with ethyl groups (–CH2CH3). When both surfaces were onlyhydrogen terminated, no chemical reactions were observed at any load or ineither sliding direction examined. Chemically attaching the ethyl groups to theupper surface and repeating the sliding simulations under moderate loads(33 GPa) resulted in chemical reactions when sliding in both directions. In the[112] direction, a complex series of chemical reactions was typically initiated bythe shearing of a hydrogen atom from the tail of one of the ethyl groups. This freehydrogen atom reacted at the interface in a number of ways. One of the observedreaction sequences involved the free hydrogen atom abstracting a hydrogenatom from the lower diamond surface to form H2. The unsaturated sites onthe tail of the ethyl group and on the lower surface were then free to react,forming a covalent bond between the two surfaces. When the shear stress fromsliding became too great, the adhesive bond was broken and an ethylene debrismolecule was formed (figure 1). This type of debris is consistent with the type ofwear debris observed in experimental studies of the macroscopic wear ofdiamond. The observations of these simulations are particularly important inview of the fact that they are consistent with conclusions inferred, but notdirectly measured, from the experimental studies of the macroscopic friction andwear of diamond.

Harrison et al. (1993) also examined the friction of diamond(111) surfaceswith chemically bound methyl groups (–CH3) on only one of the surfaces as afunction of load and sliding direction. No tribochemical reactions were observedat any of the loads examined. Recently, quantum chemical Hartree–Fock andB3LYP methods were used to examine lateral sliding in a similar system(Koskilinna et al. 2005). In that work, two methyl groups were attached toopposing model diamond(111) surfaces (i.e. C14H24 and C23H36 clusters). Therelative energy as a function of lateral displacement of the surfaces wasmonitored at a fixed interplanar distance. During lateral movement, the carbon–carbon bond that attaches the methyl groups to the model lattices was brokenand the methyl group escaped from its position between the clusters. These





reactions were the result of the direct interaction of the methyl groups onopposing model surfaces. While no tribochemical reactions were observed in theMD simulations, the simulation geometry differed slightly from the quantumsimulations. When the simulation systems are similar, the quantum simulationsand the classical MD simulations have been shown to be in good agreement. Thiswas demonstrated in the case of two diamond(111)(1!1)-H surfaces in slidingcontact studied by both quantum (Neitola & Pakkanen 2001) and classicalmethods (Harrison et al. 1992a).

(b ) Shear-induced polymerization

As self-assembly is a viable means of controlling the physical and chemicalproperties of solid surfaces, many studies have been devoted to the developmentof thin films of functionalized molecules for optical, electronic, mechanical orbiochemical applications (Ulman 1996). Technological applications, such asmicroelectromechanical systems (Mastrangelo 1998) and magnetic storagedevices (Karis 2002), have piqued interest in the potential use of organic filmsfor boundary-layer lubricants. Monolayers formed from self-assembly, such asalkanethiols and alkylsilanes, which are covalently bonded to the substrate, maybe good candidates for boundary-layer lubricants. As a result, the mechanicaland tribological properties of self-assembled monolayer (SAM) materials havebeen studied a great deal using scanning probe microscopies (Carpick &Salmeron 1997; Liley et al. 1998; Harrison et al. 2004 and references therein; Liet al. 2005; Braun & Naumovets 2006; Brukman et al. 2006).

The properties of SAMs containing chains with diacetylene moieties have beenstudied using theAFM(Mowery et al. 1999;Cheadle et al. 2001). Because the cross-linked backbone (which is the result of exposure to UV radiation) demonstrates achromatic response to elevated temperature and stress, these structures have thepotential to be used asmolecular sensors (Enkelmann 1984; Burns et al. 2001). Theatomic-scale friction of unpolymerized diacetylene and polymerized monolayershas been examined using an AFM (Carpick et al. 1999; Mowery et al. 1999).

Chateauneuf et al. (2004) used MD simulations to examine the compression andfriction of model SAMs composed of chains containing the diacetylene moiety.Because the AIREBO potential was used, cross-linking (polymerization) of thechains during the simulation was possible (Stuart et al. 2000). An irregularamorphous carbon counterface was brought into contact with three differentmonolayers. The location of the diacetylene moieties within the chains was variedand the effects on polymerization and friction were examined. The simulationsshowed that cross-linking between chains was initiated by the mechanicaldeformation of the monolayers. The amount of polymerization and its patterndepended upon the deformation, i.e. compression or shear and the location of thediacetylenemoieties within the chains.When the diacetylenemoieties were locatedin the middle of the chains, compression with the counter surface led topolymerization between monolayer chains only. When these moieties were onthe ends of the chains, chemical reactions with the counterface also occurred.Altering the placement of the diacetylene moieties by one carbon atom within thechain, i.e. the spacer length, led to different polymerization patterns withinthe monolayers.





(c ) Amorphous carbon films

Amorphous carbon and DLC films have a rich variety of structuresand frictional properties that depend upon the deposition method used tocreate them. For instance, the friction of most DLC films increases sharplywith time in inert environments while some DLC films exhibit super low frictionwhen tested under similar conditions (Erdemir & Donnet 2001; Fontaine &Donnet 2007).

The tribology between a diamond(111)(1!1)-H surface and an a–C film wasexamined using classical MD simulations (Gao et al. 2002, 2003; Schall et al.2007) and the REBO potential (Brenner et al. 2002). The effects of filmthickness and sp2-to-sp3 ratio were examined. A detailed analysis of one of thesliding simulations (thin film system) showed that the simulated frictionincreased at the start of the simulation, oscillated about some average value,underwent a transition to lower friction and finally oscillated about a loweraverage friction value for the remainder of the simulation (figure 2). Thisbehaviour is reminiscent of the experimentally observed phenomenon of ‘run-in’. An analysis of the thin film structure during sliding revealed that theinitiation of sliding caused alignment of the carbon–carbon bonds within thefilm in the sliding direction. Continued sliding and interaction with the atomson the counterface caused oscillations in the number of carbon–carbon bondsoriented in the sliding direction. These oscillations have the same period as thefriction which corresponded to the distance between hydrogen atoms on thecounterface. Sliding also caused bonds to be broken and formed within the film(intra-film reactions) and between the film and the counterface (inter-filmreactions). When the inter- and intra-film reactions ceased, the average frictionwas reduced. In other words, the film underwent restructuring to a lowerfriction state. In this study, inter-film reactions in the thin film system wereinitiated by the shearing of a hydrogen atom from the counterface above acritical load. Inter-film reactions can be initiated at lower loads by providingunsaturated atoms for reaction. Chemical reactions between the film andthe counterface increase friction by increasing adhesion between the film andthe counterface. This can be achieved by systematically removing hydrogenatoms from the diamond counterface or reducing the surface passivation(Gao et al. 2002).

The friction between two DLC surfaces has been examined using MD. In thatwork, a H-terminated DLC counterface, composed mostly of sp3-hybridizedcarbon, was placed in sliding contact with three DLC films (an analysis of filmstructure is given in Schall et al. (2007)). Three DLC films were investigated; ahydrogen-free film (P00), a film containing 20% hydrogen (P20) and a filmcontaining 38% hydrogen (P38). The key aspect of these films is that hydrogen wasuniformly distributed inside the films. This is in marked contrast to films withhydrogen-surface passivation. These three films had relatively low sp3 : sp2 ratiosbut showed no indication of graphite-like layering. The DLC counterface wasbrought into sliding contact with each of the three films and the friction as afunction of load was calculated (figure 3a). The friction versus load data clearlyshow that passivating the amorphous carbon films with hydrogen reduces friction.The friction of the hydrogen-free (P00) film is higher than the hydrogen-containing films due to covalent bond formation (adhesion) between the



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(a)

(b)

Figure 2. (a) The friction and (b) tribochemical reactions as a function of sliding distance for thethin film system (Gao et al. 2002). In (b), the top two lines represent intra-film bonds that areformed (top) and broken (second from top), respectively. The bottom two lines represent inter-filmbonds that are formed (third line) and broken (fourth line), respectively.



counterface and the film. As in the case of two H-terminated diamond surfaces,when two DLC surfaces are in sliding contact, peaks in the friction are correlatedwith increases in vibrational excitation of the bonds within the film, whichmanifests itself as an increase in temperature. This is apparent in the plots offriction and temperature as a function of sliding distance shown in figure 3b. Themaxima in the friction are immediately followed by an increase in the film’stemperature. The region of the film closest to the interface experiences the largestincrease in temperature. Closer examination of this film reveals that there is onepoint that is rougher (higher) than the rest of the film. It is the interaction of thisarea with the counter surface that is responsible for the spikes in the friction force.Thus, the periodicity in the friction force is that of the roughness of the counterfaceand not associated with any crystallographic spacing.

Simulations of friction between two DLC surfaces, as well as the earlysimulations of diamond(111)(1!1)-H against DLC illustrate the importance ofsurface passivation. High friction in DLC films arose from chemical bond formationbetween the surface and counterface due to a lack of passivation. In our earlierwork,this was termed as the adhesive component of friction which is analogous to theadhesion that occurs when two diamond surfaces are brought into contact. This





adhesion has been studied using classical MD simulations (Harrison et al. 1992b)and more recently by first-principles DFT calculations (Ciraci et al. 2007). Theclassical MD studies examined the adhesion between infinite diamond(111)surfaces with varying amounts of hydrogen and between a H-terminated diamondasperity and an infinite diamond(111) surface. In both cases, the removal ofhydrogen atoms caused the creation of unsaturated sites, or dangling bonds, thatserved as initiation points for adhesion (covalent bond formation) between the twocontacting bodies. The first-principles DFT calculations between diamond(001)slabs confirmed the importance of hydrogen in passivating diamond surfaces andprovided additional insight into the charge distribution for H-terminated andhydrogen-free surfaces.

(d ) Quantum MD

The frictional properties of the antiwear additive zinc dialkyldithiopho-sphate (ZDDP) were recently examined using Car–Parrinello ab initio MDsimulations (Mosey et al. 2005). The response of antiwear additives to extremetribological conditions (large flash pressures pmax and temperatures Tmax) wasinvestigated by examining the response of bulk zinc phosphate to various valuesof pmax. The simulation cells were composed of one triphosphate (P3O10H5) andone or two zinc phosphate molecules (Zn[PO4H2]2) with periodic boundaryconditions imposed. This choice of starting conditions models the decom-position products of the antiwear additive ZDDP. The simulations were carriedout by linearly increasing the pressure until some predetermined value of pmax

was reached. Once pmax was reached, the pressure was decreased at the samerate. The results of all the simulations were in general agreement, irrespectiveof compression rate, initial alignment of molecules, temperature or system size.The application of pressure greater than approximately 6 GPa caused cross-linking of the system where the Zn sites adopted a tetrahedral geometry. Anadditional increase in pressure (approx. 17 GPa) produced a highly cross-linkedconfiguration in which the Zn was hexacoordinate. This structure exhibitedthree-dimensional cross linking (figure 4). When the pressure was reducedbelow approximately 7 GPa, the Zn returned to its tetracoordinate state. Theformation of the cross-linked networks increased the bulk modulus and shearmodulus of the films. This is consistent with the experimental data, whichshow that the harder one pushes on these films the harder they become (Becet al. 1999).

6. Links between friction, structure and disorder in SAMs

The frictional properties of SAMs have been studied extensively using scanningprobe microscopies (Carpick & Salmeron 1997; Gnecco et al. 2007). The effects ofchain length, packing density and terminal group on friction are some of thevariables that have been examined. This experimental work has motivated anumber of theoretical studies of the friction of SAMs. For a more completereview of this theoretical work, the reader is referred to Harrison et al. (2004).



–4

0

4

8

12

0 20 40 60 80 100 120fr

ictio

n (n

N)

280

300

320

340

360

380

400

T(K

)sliding distance (Å)

(i)

(ii)

P38

300

250

200

150

100

50

–50

0

0 20 40 60 80 100 120 140load F7 (nN)

fric

tion

F×

(nN

)(a) (b)

Figure 3. (a) Friction force as a function of applied load when a DLC tip is in sliding contact witha-C films with different amounts of hydrogen (red solid line, P00; green dashed line, P20; and bluedotted line, P38). (b) (i) Temperature and (ii) friction force as a function of sliding distance when aDLC tip is in sliding contact with the P38 (DLC) film. The load is held constant at 0 nN.The upper region of the surface represented by the blue line in (i) is closest to the sliding interface(red solid line, bottom; green dashed line, middle; blue dotted line, upper).



(a ) SAMs with ideal packing

For alkanethiols on Au(111), multiple experiments have found theorientation of the chains to be in an all-trans conformation with a cant of 308(Ulman 1996). This arrangement of chains serves as the ideal geometry andis the starting point for many simulations that have examined the frictionof SAMs (Harrison et al. 2004). For example, Mikulski & Harrison (2001b)used classical MD simulations and the AIREBO potential to examine theperiodicities associated with sliding a diamond(111)(1!1)-H surface across amonolayer composed of alkane chains. Chains with 13 carbon atoms werechemically bound to a diamond(111) surface in the (2!2) arrangement yieldingapproximately the same packing density and cant as observed in monolayerscomposed of alkanethiols on Au(111). It should be emphasized that thesesimulations correspond to an ideal case because the counterface is atomicallyflat and commensurate with a tightly packed, and nearly defect free, monolayer.This idealized situation gives rise to many periodic properties associated withsliding, some of which are discussed below.

In these simulations, the rigid layers of the diamond(111)(1!1)-H counter-face were moved towards the monolayer at a constant velocity to apply a load.After equilibrium was established at a given load, the rigid layers were moved ata constant velocity in the sliding direction. During the course of sliding alongthe direction of chain cant, the following quantities were monitored: the forcevector exerted by the counterface on the full monolayer of chains; the positions



Figure 4. Representative structure of the cross-linking of the zinc phosphate system that occurswhen compressed to approximately 17 GPa. The zinc atoms are hexacoordinate in all cases;however, some of the bonds corresponding to interactions between atoms in periodically repeatedcells are not shown. Blue, purple and red spheres correspond to zinc, phosphorus and oxygenatoms, respectively. (Adapted with permission from Mosey et al. (2005).)



of the terminal carbon atoms within each chain; the change in length of thecarbon backbone of each chain; the total energy of the system E (kineticCpotentialCwork done by bath); and the azimuthal angle f, which was taken tobe the average angle between the sliding direction and the projection of eachcarbon backbone in the plane that contains the monolayer. As the counterfaceslides over the monolayer, analysis of the angle f showed the chains gettingpushed from side to side as each wave of the hydrogen atoms of the counterfacepassed by. Animated sequences of the simulation revealed that all chains moveto the same side in a synchronized motion. The motion is not symmetric aboutzero (though it does pass through zero); this shows that the chains werepreferentially shifted to one side. Thus, it is only after sliding through one unitcell that the chains returned to the starting geometry. The same periodicity wasobserved in a number of quantities, with some examples shown in figure 5. Aseach wave of hydrogen atoms from the counterface interacts with the top of thechain during sliding, the chains were slightly compressed and stretched. Whenthe counterface hydrogen atoms passed by the top of the chains, the chainssprang back to the uncompressed, unstretched state. The stretching out in thesliding direction extended throughout the entire chain. This is also known as the‘stick’ in the atomic-scale stick–slip phenomenon. During the spring back phase,or the slip, the friction force Fy changes sign, and decreases dramatically, as thechains push the counterface hydrogen atoms (figure 5). It is important to notethat the fluctuations in the friction force are significantly larger than the



0

20

0 1 2 3 4 5 6 7 8

E (

eV)

sliding distance / unit cell length

–12

12

–80

–50(a)

(b)

(c)

Figure 5. Average system energy E, friction Fy and normal forces Fz on the counterface as afunction of sliding distance. The average load on the system is 64 nN (approx. 8 GPa). The slidingdistance has been divided by the unit cell length of the (2!2) packing of the chains. Adapted fromMikulski & Harrison (2001b).



average force. The implication being that while the motion of the counterface onthe whole is steadily depositing energy into the system (slope of E in figure 5),at any given instant it can either be depositing or removing energy to thissystem depending on whether it is pushing the chains or being pushed by them.This is evident in figure 5, which shows the total energy of the system E. Theperiodicity associated with Fy is very regular implying that the channels forenergy dissipation associated with this force should exhibit this extremelyregular periodic behaviour.

All the periodic quantities associated with sliding exhibited a start-upsliding effect with the final shape of the period oscillation achieved after two orthree unit cells. This sort of start-up effect is also apparent in the simulationsof two, well-ordered hydrocarbon monolayers on SiO2 in sliding contact(Chandross et al. 2004). In the analysis of kinetic friction, data from these firstfew cycles should be ignored. This effect can be avoided by equilibrating thesystems while sliding (Mikulski et al. 2005a,b). This method has the addedadvantage of allowing for some settling of the disorder caused by therandomness associated with the compression of the monolayer by an infinitesurface. Anytime the counterface is commensurate with a tightly packedmonolayer, periodicities in the properties associated with sliding, like stick–slip, will be apparent. Classical MD simulations of two alkylsilane monolayersin sliding motion exhibit atomic-scale stick–slip with the same periodicity asthe monolayer for all the velocities examined (Chandross et al. 2002). Themagnitude of the oscillations can be enhanced by increasing the strength of theattraction between the monolayers and the counterface. This was demon-strated nicely by Park et al. (2003) in their examination of the friction betweenopposing alkanethiol SAMs with –CH3, –OH and –COOH terminations(figure 9).



0

10

20

30

40

50

250 500 750 1000

fric

tion

(nN

)

load (nN)

Figure 6. Friction versus load when a diamond(111)(1!1)-H surface is in sliding contact withmonolayers composed of 72 C18 alkane chains. Data represented by the black solid line is forchains attached to diamond(111) in the (4!4) arrangement. All other systems had the chainsattached in the (2!2) arrangement. The tightly packed system (grey dashed line) has 72 chains.Twenty and forty (2!2) chains have been randomly removed from the surfaces represented bythe black dashed and grey solid lines, respectively. Adapted from Mikulski & Harrison (2001a)and Harrison et al. (2004).



(b ) Structural effects and disorder

It is important to note that the MD simulations described above used idealizedgeometries, which can be difficult to attain experimentally. Even in well-packedalkanethiol SAMs, with a chain-to-chain spacing of approximately 5 A, domainsand defects exist (Ulman 1996). In addition, decreasing the length of the alkanechain changes the packing density of the alkanethiol SAMs. It is also possible tomake SAMs with chains of mixed lengths. Therefore, while the examination ofidealized geometries using computer simulations yields important information,there is a need to examine systems which fall outside this classification. Some ofthe variables that have been examined are packing density (or defect density)(Mikulski & Harrison 2001a; Chandross et al. 2004; Harrison et al. 2004), mixedchain lengths (Mikulski et al. 2005a), the odd–even effect (Mikulski et al. 2005b)and surface termination (Park et al. 2003).

Mikulski & Harrison (2001a) examined the effects of packing density, or defectdensity, in SAMs by randomly removing 20 chains (approx. 30%) from amonolayer composed of C18 alkane chains on diamond. The idealized monolayer,composed of 72 tightly packed chains in the (2!2) arrangement, served as thecontrol system. The diamond(111)(1!1)-H surface was always used as thecounterface. Additional defect densities and packing arrangements were alsoexamined and friction results with double the defect density for a (4!4) packingarrangement were very similar to the data for the monolayer with approximately30% defects (figure 6; Harrison et al. 2004). The creation of defects within themonolayer disrupts both the tight packing of the monolayer and the concertedresponse of the chains to the motion of the counterface, which leads to higherfriction. As a result, the friction force as a function of sliding distance loses the



(a)

(b)

forc

e di

stri

butio

n

0 120 240 360

forc

e di

stri

butio

nazimuthal angle (deg.)

6

4

2

0

6

4

2

0

1 2 3 4 5 6 7 8 9sliding distance / unit cell length

(i)

(i)

(ii)

(ii)

Figure 7. (a) Friction force versus sliding distance for monolayers composed of (i) C13 (odd) and(ii) C14 (even) (SAM) alkane chains. The sliding distance has been divided by the (2!2) unit celldistance of diamond. The load of 40 nN corresponds to 1.8 GPa. (b) Contact force distributions forthe three terminal hydrogen atoms in each chain as a function of azimuthal angle when anamorphous carbon counterface is in sliding contact with (i) odd and (ii) even monolayers(figure 8a). Friction (green line) is the sum of the resisting (positive) and pushing (negative)contact forces (black, load; red, resist; green, net; blue, push). A detailed description of the contactforces is given in Mikulski et al. (2005b).



periodicity associated with the (2!2) unit cell and the average friction is higher(Mikulski & Harrison 2001a). The effect of defect density on the friction betweentwo SAMs composed of alkane chains attached to SiO2 was examined byChandross et al. (2004) using MD and the COMPASS force field. Frictionbetween commensurate, defect-free SAMs and SAMs with 10, 30 and 50% of thechains randomly removed was examined. The periodicity of properties like shearstress, as a function of sliding distance, was also destroyed by the creation ofdefects in the opposing SAMs.

Even slight disruptions within the monolayer, or breaking of thecommensurability between the monolayer and the counterface, perturb theregular periodic shape of the friction force as a function of sliding distance. Forexample, Mikulski et al. (2005b) used a H-terminated, amorphous carboncounterface and MD to examine the friction model of SAMs composed of C13

alkane chains (referred to as the odd system) or C14 chains (referred to as theeven system) attached to diamond(111) in the (2!2) arrangement (figure 8a).The friction response of these monolayers was examined over the load range20–320 nN (0.9–14.4 GPa). The counterface was incommensurate with themonolayers and nominally flat to minimize roughness effects. Because thecounterface is no longer commensurate with the monolayer, the friction as afunction of sliding distance becomes slightly more irregular than the perfectlyrepeating patterns shown in figure 5. While the friction force versus time



(a)

force interval (nN)

–0.8 –0.4 0.4 0.80

(b)

(i)

(ii)

Figure 8. (a) H-terminated amorphous carbon counterface (top) in contact with a monolayer of C14

alkane chains attached to diamond(111) in the (2!2) arrangement. (b) Contact force distributionsin the sliding direction for the top 100 –CH3 and top 100 –CH2– chain groups for pure (C14 chains)and the top 200 groups for the mixed monolayers. The sliding direction is along the direction ofchain cant and transverse to the chain cant in (i) (red, pure; green, mixed) and (ii) (blue, pre-transition; pink, post-transition), respectively. Positive forces correspond to chain groups resistingcounterface motion, while negative (restoring) forces indicate groups pushing the tip along. Forsimulation details see Mikulski et al. (2005a).



for the C14 monolayer is periodic (figure 7a), it has more structure than whenthe commensurate, atomically flat diamond counterface was used. Changingthe number of carbon atoms in the chains to 13, introduces slightly moredisorder at the interface (Mikulski et al. 2005b) and, as a result, the frictionversus sliding distance plot for this system at the same load is less regular thanit is for the monolayer composed of C14 chains (figure 7a). The application ofload to the odd system resulted in more structural changes at the interfacethan in the even system. As a result, the friction versus time at higher loads(figure 7a) of the even system is still somewhat ordered; however, these dataare less ordered in the odd system.

Mikulski et al. (2005b) also found that the average friction of the odd systemwas higher than the friction of the even system at all but the lowest loadsexamined. The difference in friction between these two systems was ultimatelyattributed to structural differences in the monolayers at the sliding interface.An analysis of the contact forces on the terminal hydrogen atoms of each chainrevealed interesting differences in the way load and friction forces aredistributed in the even and odd systems (figure 7b). In the even system, thehydrogen atom that is protruding into the monolayer, below its parent carbonatom, has no contact forces on it. The peak at 1808 corresponds to the H atomthat is the highest distance above the monolayer. This H atom carries most ofthe load and contributes a negligible amount to the net friction. The thirdH atom has a larger contribution to the friction but carries only a small amount





of the load. In contrast, in the odd system, all three of the terminal hydrogenatoms had appreciable contact forces although the forces on one hydrogen weresmall. There was an interesting interplay between the two hydrogen atoms withthe largest forces with one of these atoms predominately resisting tip motionwhile the other assists tip motion. Taken together, these two hydrogen atomswere responsible for most of the friction.

There are many ways to introduce disorder in a SAMs-containing system, whichdisrupts the periodicity of the friction versus sliding distance data and ultimatelyincreases the friction. Perry and co-workers (Lee et al. 2000) used an AFM toexamine the friction of SAMs composed of spiroalkanedithiols. The use of this typeof molecule allows the effects on friction of crystalline order at the sliding interfaceto be unambiguously probed. The spiroalkanedithiol molecules attach to thesubstrate and then branch into two chains. Systematically shortening one ofthe chains caused a progressive increase in disorder and an increase in friction.

Motivated by experimental work that examined the friction ofmixed chain lengthSAMs, Mikulski et al. (2005a) usedMD to investigate monolayers of n-alkane SAMscomposed of chains of a single length (pure) and those composed of chains of twolengths (mixed). As in previous studies, the chains were chemically bound toa diamond(111) substrate in the (2!2) arrangement and the amorphoushydrocarbon counterface shown in figure 8a was used to probe friction. The puresystemwas composed of 100C14 alkane chains and themixed systemcontained equalamounts of C12 and C16 alkane chains. The connection between contact forces,between the counterface and the chain groups, during sliding and the structure andmobility of the monolayer chains was examined. Structural differences, or disorder,at the sliding interface caused both the friction force and the average deviation in theposition of the ends of the chains in the mixed system to loose periodicity. The netfriction of the mixed system was higher. The individual contact forces on the top100 –CH3 and –CH2 groupswithin each chainwere plotted as a histogram (figure 8b).The shape of the contact force distributions containing the positive forces is similar inboth the pure and mixed systems. Therefore, the pure and mixed systems resist themotion of the counterface in a similar way. In contrast, the negative (forces that‘push’ the tip along) contact forces of the pure and mixed systems are markedlydifferent. This suggests that the ordered structure of the pure systems is conduciveto returning the energy stored during resistive processes as mechanical energyto the monolayer, while the disordered, slightly less dense, structure of the mixedsystems at the sliding interface results in the conversion of the stored potentialenergy into thermal energy. The resistive forces at medium to high force intervalsindicate that the scale of forces is similar in the pure and mixed systems. Whilethe larger forces in the pure systems at small positive force intervals indicate a moredensely packed structure that brings more chain groups in more frequent contactwith the tip. With its densely packed structure, the groups in the pure monolayerexhibit a much higher level of symmetry between positive and negative forces alongthe sliding direction (figure 8b). As a result, when the positive and negative forcesare added, the net friction is small. The positions of chain groups in themixed systemasa functionof timevary over amuchwider range than the groups in thepure system.This points to a correlation between restricted range of motion and lower frictionwith the coordinated response of chains during sliding in the pure system aidingin the recovery of mechanical energy, which leads to low net friction.





(c ) Friction anisotropy

The AFM and related force microscopies have been used to measure frictionanisotropy in a number of systems, including SAMs (Carpick & Salmeron 1997;Carpick et al. 1999; Chen et al. 2006). For example, Liley et al. (1998) used a lateralforcemicroscope tomeasure frictionof a lipidmonolayer in thewearless regime.Themonolayer contained domains with long-range orientational order and largerfriction anisotropies and non-negligible friction asymmetries were measured. MDsimulations have also been used to examine the dependence of friction on slidingdirection in the pure and mixed SAMs described above (Mikulski et al. 2005a). Atthe beginning of the slides, the cant of chain backbones is nearly perpendicular tothe sliding direction. In this work, four independent starting configurations wereexamined for both the mixed and pure systems. Upon sliding transverse to chaincant, all four of the mixed systems underwent a transition corresponding to arotation of 608 of the chains within the monolayer. After the transition, the cant ofthe reoriented chains was more closely aligned with the sliding direction. Incontrast, only two of the pure systems successfully transitioned to this new chainorientation in the same sliding distance.

Both the mixed and the pure systems exhibited higher friction when slidingtransverse to the chain cant, compared to sliding in the direction of chain cant. Thisis apparent from examination of the contact force distributions for the pure systemwhen sliding transverse to the tilt direction (figure 8b). Before the collectiverotation of the chains (pre-transition), the forces resisting the motion of thecounterface are larger than when sliding with the chain cant. In addition, there is asignificant asymmetry between the resistive and restoring (negative) forces thatleads to a net friction that is a factor of two larger than it is when sliding along thechain cant. Once the chains have been realigned in the sliding direction (post-transition), the contact force distribution changes and more closely resembles thedistribution of the pure system when sliding along the chain cant.

(d ) Chemical effects

One interesting way to examine the chemical contributions to friction is tocompare the friction of SAMs with different chemical species on the ends ofthe chains while using the same tip to probe the samples. The effectof fluorination on friction was examined using an AFM by comparing theresponse of –CH3– and –CF3-terminated SAMs (Kim et al. 1999; Houston et al.2005). The effect of –OH termination (Brewer & Leggett 2004) and –COOHtermination (Houston & Kim 2002) on friction has also been examined. Parket al. (2003) used MD to examine the friction between two monolayers ofalkanethiol SAMs with –CH3, –COOH or –OH termination. Initially themonolayers were in their ideal packing geometry. The all-atom COMPASSforce field was used, which allows for partial charges that arise fromelectronegativity differences between atoms but does not allow for chemicalreactions. Both the –CH3 and –COOH-terminated films exhibited stick–slip(figure 9). The periodicity of the –COOH-terminated chains corresponded to theperiodicity of the chains because the sticking was due to hydrogen bonding acrossthe sliding interface. When the chains were –CH3 terminated, the terminal C–Cbond is nearly parallel to the substrate. As a result, both the terminal –CH2– and–CH3 groups interacted with the opposing monolayer resulting in a smaller



321

P ⊥(G

Pa)

P ⊥(G

Pa)

P ||(G

Pa)

P ||(G

Pa)

0–1

3210

–1

210

–1

210

–10 5 10 15 20 25 30

sliding distance (Å)

(a)

(b)

(c)

(d )

Figure 9. Friction between alkanethiol films. (a) Normal stress and (b) shear stress for (CH2)8CH3

chains; (c) normal and (d ) shear stress for (CH2)8COOH chains. See Park et al. (2003) forsimulation details.



periodicity than the spacing between chains. The increased adhesion between the–COOH-terminated monolayers from the hydrogen bonding is responsible for thelarger fluctuations in the shear stress, compared to the –CH3-terminated chains.

7. Summary and outlook

Since the positions and velocities of all atoms are known at each time step, MDsimulations can provide unique atomic-scale insight into processes that occur atsliding interfaces. In this review, we have highlighted some of the insights that haveshed light on the friction of SAMs, carbon-containing systems and antiwearadditives. While it is true that the length and time scales of AFM experiments andMD simulations do not correspond exactly, much insight into experimental datacan still be provided by MD. Increases in computational power and algorithmdevelopment (e.g. hybrid finite element and MD simulations) continue to increasethe time and length scales available to simulations. At the same time, uniqueexperimental methods to probe the interface during sliding at smaller and smallerlength scales continue to be developed. Thus, the gap between experiments andsimulations continues to narrow. Continued work in these areas will provide thetools that will allow for the fundamental origins of friction to be unlocked.

J.D.S., J.A.H. and G.G. acknowledge the support from AFOSR under contracts

F1ATA053001G001 and F1ATA053001G004 (Extreme Friction MURI). J.A.H., M.T.K. and

P.T.M. acknowledge the support from the ONR under contract N0001406WR20205. J.A.H. thanks

N. Mosey and M. Chandross for providing figures from their work.

U.S. Government Employee Certification: this will certify that all authors of the work are U.S.

government employees and prepared the work on a subject within the scope of their official duties.

As such, the work is not subject to U.S. copyright protection.





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